Here's the little I have on this company. We might learn more from a study of antebellum Mobile newspapers.

First organized at Mobile, Alabama, October 6, 1846, this command mustered in state service on March 21, 1861. It had previously been in state service for sixty days, beginning January 3, 1861. Officers and men enlisted in Confederate service at Mobile, Alabama, April 23, 1861.

There's a book on this company:
Coker, William S., editor. The Mobile Cadets, 1845-1945: A Century of Honor and Fidelity. Bagdad, Fla.: Patagonia Press, 1993.

This might be useful:
"A sketch of 12 months service in the Mobile Rifle Company
by an unidentified member," Al. Historical Quarterly, XXV (1963), pp. 149-189.

This man was a company member:
Henry Hotze / Three Months in the Confederate Army (University, AL: University of Alabama Press, 1962)

This article might be useful:
Rodgers, Thomas G. "The 'Bandbox' Soldiers of the 3rd Alabama Infantry Became Combat-Hardened Veterans in Virginia." America's CW (Jul 1990): pp. 12, 14 and 16.

Here's a detailed article on Capt. Sands. It leaves me with the impression that many cadets were students at Spring Hill College:
http://www.genealogy.org/~ajmorris/cw/sands.htm

Here's a well-known 1859 picture being auctioned:
http://page.auctions.shopping.yahoo.com/auction/51924367

And something concerning a member and a pre-war flag:
http://www.archives.state.al.us/referenc/FLAGS/109.html